To John Conwill   September 1842

<beginning of letter missing>

Your solution of my query is faultless, I cannot however say this with respect to your solution of the one which related to bodies falling upon the earth¹ – That gravitation exists at the earth’s centre I allow, but that it exists there exclusively I deny. attraction is an infusion for a share of which each particular particle of matter can claim.

Let the earth be a perfect sphere, a body descending thro’ it, say at ‘A’ is pulled downwards, if I may so speak, with a force due to the distance ‘ab’ – it is pulled upwards by a force due to the distance ‘ac’ and it descends with a force equal to the difference of these (abstracting the idea of its preacquired momentum) until it comes to the earth’s centre ‘O’ where the difference is nothing and there it will remain.

You have virtually admitted this in the query which you attached to your last letter*² – for, if attraction existed exclusively at the earth’s centre there would be no difficulty in conceiving that a body would wend its way to the spot without turning to the right or left –

A ******A. Let ‘a’ be the N pole³ of the earth. if a body be let drop from it – abstracting the idea of density from the earth, but letting attraction and extension remain as at present – it will pass on in a straight line to the earths centre – it is evident that an equilibrium

of attraction exists at each side of the body (supposing the earth to be of uniform density) that is, as it is as much attracted towards ‘b’ as towards ‘c’ – towards ‘d’ as towards ‘e’, it is evident I say that it will not deviate from a straight course downwards to the centre ‘o’

But let us remove it from the pole to the latitude mentioned – say to ‘g’ – the case is now altered, let us assume a point ‘h’ in the straight line from ‘g’ to ‘o’ and let us conceive the body to be situated there and enquire how it is affected by gravity – draw the parallel ‘lhf’ – it is evident now that the face of attraction at ‘b’ is greater than at ‘c’ because the greater number of attracting particles exist at that side, and if we assume any other two corresponding points we shall have a like result, therefo’ I conclude that the attractive force at the side ‘b’ over balances that on the side ‘c’ – hence the body cannot proceed in a straight line to the earths centre but will describe the curve ‘gKo’ - - -

*To determine the line a body will describe if let fall from 54° 22’ N latitude supposing it could pass in vacuo’⁴ to the earths centre –

– But C. did not assert that gravity existed exclusively at the earths centre the argument in the former part of thy extract is the result of a misconception of my own

J Tyndall

RI MS JT 2/1/164–3